JAMB Mathematics Past Questions & Answers - Page 323

1,611.

The sum to infinity of a geometric progression is \(-\frac{1}{10}\) and the first term is \(-\frac{1}{8}\). Find the common ratio of the progression.

A.

\(-\frac{1}{5}\)

B.

\(-\frac{1}{4}\)

C.

\(-\frac{1}{3}\)

D.

\(-\frac{1}{2}\)

Correct answer is B

Sr = \(\frac{a}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8} \times \frac{1}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8(1 - r)}\)

\(-\frac{1}{10}\) = \(\frac{1}{8 - 8r}\)

cross multiply...

-1(8 - 8r) = -10

-8 + 8r = -10

8r = -2

r = -1/4

1,612.

The nth term of a sequence is n2 - 6n - 4. Find the sum of the 3rd and 4th terms.

A.

24

B.

23

C.

-24

D.

-25

Correct answer is D

n2 - 6n - 4

For the 3rd term,
32 - 6(3) - 4

9 - 18 -4 = -13

For the 4th term,
42 - 6(4) - 4

16 - 24 - 4 = -12

Sum of both terms

-13 - 12 = -25

1,613.

Find the range of values of m which satisfy (m - 3)(m - 4) < 0

A.

2 < m < 5

B.

-3 < m < 4

C.

3 < m < 4

D.

-4 < m < 3

Correct answer is C

(m - 3)(m - 4) < 0

(m - 3) < 0 ; (m - 4) < 0

m < 3 ; m < 4

3 < m < 4

1,614.

The value of y for which \(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\) is

A.

\(y > \frac{2}{3}\)

B.

\(y < \frac{2}{3}\)

C.

\(y > -\frac{2}{3}\)

D.

\(y < -\frac{2}{3}\)

Correct answer is C

\(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\)

Collect like terms

\(\frac{y}{5} - \frac{y}{2} < \frac{2}{5} - \frac{1}{5}\)

\(\frac{2y - 5y}{10} < \frac{2 - 1}{5}\)

\(\frac{-3y}{10} < \frac{1}{5}\)

\(y > \frac{-2}{3}\)

1,615.

U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3

A.

24

B.

27

C.

32

D.

36

Correct answer is A

U \(\propto \frac{1}{V^3}\)

U = \(\frac{k}{V^3}\)

k = UV\(^3\)

k = 81 x 2\(^3\) = 81 x 8

When V = 3,

U = \(\frac{k}{V^3}\)

U = \(\frac{81 \times 8}{3^3}\)

U = \(\frac{81 \times 8}{27}\) = 24